Over the last decade, several papers have been published on the contribution of the Theory of Constraints (TOC) and Throughput Accounting to product mix decisions. In these papers, the quality of the TOC-based approach to generate good or even optimal solutions is assessed with very different results, particularly when compared with other product mix decision tools. It is the objective of this article to expose the often, not explicitly revealed, premises that are mandatory for generating optimal product mix decisions using a TOC-based approach. By analysing several examples, which are modifications of one and the same basic example, premises on the solution space and the objective function are examined and conclusions made, which are shown in a checklist at the end of the paper. If more than one binding multi-product constraint occurs, optimal product mix decisions can only be derived in special cases. Also, the assumption of integer solutions may lead to non-optimal TOC-based solutions. Furthermore, a correct cost allocation is mandatory, even if sometimes not easily conductible. In particular, taking into account only (all) material costs may lead to wrong decisions. Finally, it is shown that discontinuities in the objective functions deriving, for example, from price discounts, may affect the product mix decision and require special modifications of the TOC-based approach.